Created: Oct. 3, 2024, 3:23 p.m.

Last Updated: Dec. 8, 2024, 3:24 p.m.

This project visualises the Mandelbrot set using Python and Matplotlib. The Mandelbrot set consists of complex numbers for which the iterated sequence z_(n+1) = z^2_n + c remains bounded when starting from z_0 = 0. The boundary of the Mandelbrot set exhibits fractal geometry, with self-similarity and infinite complexity.

This visualisation allows for adjustable iteration depth, controlling the number of times each point in the complex plane is iterated. Points within the set, where the sequence remains bounded, are coloured black, while those diverging are assigned colours based on the rate of divergence. The colouring algorithm highlights the fractal’s boundary, revealing structures related to the density of escape times for points just outside the set.

This project provides a tool for examining the local behaviour of complex dynamics around the Mandelbrot set, but also is just something fun because the set is just really cool to look at.

- Technologies Used: Python

- Project Type: Data Visualization, Mathematical Modelling

View Code